Sequence and series word problem

[Aya]

Tod injured his wrist while he was skateboarding. To relive the pain his doctor prescribed him some medication. He takes 500mg of medicine every 6h. Only 25 % of the medication remains in his body by the time he is ready to take another pill.
Write and equation to model this.


so 25% is left in his body that means that 75% was used up.

so 25%, 125%, !50%

...thats wrong right?

I don't know what to do...

 

[pizzasky]

After Tod takes the first round of medication, he has 500 mg of medicine in his body.

Six hours later, he has (0.25 x 500)mg of medicine from the previous round remaining in his body, as well as another dosage of 500mg.

Another six hours later, he has (0.25)(0.25 x 500 +500)mg of medicine from the previous rounds remaining in his body, as well as another dosage of 500mg.

Try to observe a pattern here and see if you can fit a certain distribution into part of your final equation!

 

[HallsofIvy]

Tod injured his wrist while he was skateboarding. To relive the pain his doctor prescribed him some medication. He takes 500mg of medicine every 6h. Only 25 % of the medication remains in his body by the time he is ready to take another pill.
Write and equation to model this.


so 25% is left in his body that means that 75% was used up.

so 25%, 125%, !50%

...thats wrong right?

I don't know what to do...

To "relive" the pain?? What an evil doctor!

so 25%, 125%, !50%

...thats wrong right?

What's right with it? What do 25%, 125%, 150% mean? You were asked to write an equation and that is not an equation! Let f(t) be the amount of medication in his body, in mg, after t hours. You know
f(0)= 500 and f(6)= (0.25)(500)= 125. That's not enough to information without at least knowing the "type" of function. The simplest assumption is that f(t) is linear: f(t)= mt+ b for some numbers m and b.
Then f(0)= m(0)+ b= b= 500 and f(6)= m(6)+ b= 125. Find m and b.

A more realistic assumption would be an "exponential function": f(t)= Ca^t so that f(t)= Ca⁰= C= 500 and f(6)= Ca⁶= 125. Find C and a.

Now, you have to decide whether to use one of those or another "type" of function. Are you told anything more about the function? Is this chapter of your book about linear functions or exponential functions?

 

[Aya]

Its supposed to be sequences and series

so what I was doing was finding the % of medicnin that was in his body, but I guess this approach was wrong

So I have to find the amount of medicin that is in his body

So...

t0=5oomg
t1=625mg
t2=656.25

Then
tn-1 x 0.25+500
would be the recursave fomula

 

[pizzasky]

You are right in saying that the recursive formula is $$T_{n}=0.25T_{n-1}+500$$. However, this formula needs you to know what $$T_{n-1}$$ is before you can find out the value of $$T_{n}$$. Is it possible for you to find a formula which expresses $$T_{n}$$ in terms of n?

Here are some steps to guide you:

Let $$T_{n}$$ be the amount of medicine in Tod's body 6n hours after the first dosage.

So, $$T_{0}=500$$

$$T_{1}=500(0.25)+500$$

$$T_{2}=0.25(500(0.25)+500)+500$$
...

Work out an expression for $$T_{3}$$ but do not simplify it. Some re-arrangement of terms in the expressions obtained should be helpful. Then try to obtain a general equation of $$T_{n}$$ in terms of n and see if you can fit a certain series into PART of the equation. (On first glance, which series do you think is involved? If this series is involved, what should the terms in the series look like?)